Implicit Geometric Regularization for Learning Shapes

Gropp, Amos; Yariv, Lior; Haim, Niv; Atzmon, Matan; Lipman, Yaron

doi:10.48550/arxiv.2002.10099

Cited by 62 publications

(106 citation statements)

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“…Different from single-view reconstruction which is an ill-posed problem, reconstruction from discrete point clouds or coarse voxel grids leads to finer shapes due to the 3D prior knowledge provided by them inherently. Given a point cloud as input, traditional optimization-based methods such as Moving Least Square [2] and Poisson Surface Reconstruction [20,21], and deep optimizationbased methods such as SAL [3] and IGR [15], can generate a continuous surface with fine details. When ground truth point-occupancy pairs are available, implicit-functionbased methods such as OccNet [25] and ConvOccNet [29] can also address this task well.…”

Section: Related Workmentioning

confidence: 99%

TaylorImNet for Fast 3D Shape Reconstruction Based on Implicit Surface Function

Xiao¹,

Xu²,

Gao³

2022

Preprint

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Benefiting from the contiguous representation ability, deep implicit functions can extract the iso-surface of a shape at arbitrary resolution. However, utilizing the neural network with a large number of parameters as the implicit function prevents the generation speed of high-resolution topology because it needs to forward a large number of query points into the network. In this work, we propose TaylorImNet inspired by the Taylor series for implicit 3D shape representation. TaylorImNet exploits a set of discrete expansion points and corresponding Taylor series to model a contiguous implicit shape field. After the expansion points and corresponding coefficients are obtained, our model only needs to calculate the Taylor series to evaluate each point and the number of expansion points is independent of the generating resolution. Based on this representation, our TaylorImNet can achieve a significantly faster generation speed than other baselines. We evaluate our approach on reconstruction tasks from various types of input, and the experimental results demonstrate that our approach can get slightly better performance than existing state-of-the-art baselines while improving the inference speed with a large margin. Our code will be released in https://github.com/svip-lab/TaylorImNet.

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Section: Related Workmentioning

confidence: 99%

TaylorImNet for Fast 3D Shape Reconstruction Based on Implicit Surface Function

Xiao¹,

Xu²,

Gao³

2022

Preprint

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“…Graphics, has introduced machine learning methods that made possible great advances to reformulate and solve classical problems, creating new applications. Particularly, modeling shapes as level sets of neural networks has recently demonstrated to be an effective geometric surface representation [27], [24], [15], [33]. Furthermore, neural implicit models can be used to represent dynamic radiance fields with applications to high-quality rendering and animation based on real world data [28], [31], [30], [29] .…”

Section: Related Workmentioning

confidence: 99%

“…We call the zero-level set g −1 (0) a neural implicit surface. SIREN [33] and IGR [15] are examples of neural networks capable of representing smooth implicit functions.…”

Section: Neural Implicit Surfacesmentioning

confidence: 99%

“…R 3 has been considered as the domain of smooth neural implicit functions [33,15,25]. However, as mentioned in the introduction (Sec 1), we can augment R 3 by a product space R 3 × R k , where p ∈ R 3 denotes a point in the space and c ∈ R k denotes a vector that control k direction of possible animations (rigid motion, smoothing, morphing, ...) of the initial implicit surface.…”

Section: Neural Homotopiesmentioning

confidence: 99%

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Neural Implicit Surface Evolution using Differential Equations

Novello¹,

Silva²,

Lopes³

et al. 2022

Preprint

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This work investigates the use of neural networks admitting high-order derivatives for modeling dynamic variations of smooth implicit surfaces. For this purpose, it extends the representation of differentiable neural implicit surfaces to higher dimensions, which opens up mechanisms that allow to exploit geometric transformations in many settings, from animation and surface evolution to shape morphing and design galleries.The problem is modeled by a k-parameter family of surfaces Sc, specified as a neural network function f : R 3 × R k → R, where Sc is the zero-level set of the implicit function f (•, c) : R 3 → R, with c ∈ R k , with variations induced by the control variable c. In that context, restricted to each coordinate of R k , the underlying representation is a neural homotopy which is the solution of a general partial differential equation.

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“…Second, the fully differentiable learning process allows the MLP to learn complex signals from sparsely available data points to reconstruct high-quality images or objects. Recent research has demonstrated the effectiveness of coordMLPs for a wide range of signal fitting or learning tasks such as image super-resolution (Chen et al, 2021), 3D shape representation (Park et al, 2019;Mescheder et al, 2019;Gropp et al, 2020), novel view synthesis Schwarz et al, 2020) and photo-realistic 3D scene editing (Niemeyer & Geiger, 2021). The search for more accurate and generalizable implicit neural network architectures and methodologies is an active area of research.…”

Section: Introductionmentioning

confidence: 99%

CoordX: Accelerating Implicit Neural Representation with a Split MLP Architecture

Liang¹,

Sun²,

Vijaykumar³

2022

Preprint

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Implicit neural representations with multi-layer perceptrons (MLPs) have recently gained prominence for a wide variety of tasks such as novel view synthesis and 3D object representation and rendering. However, a significant challenge with these representations is that both training and inference with an MLP over a large number of input coordinates to learn and represent an image, video, or 3D object, require large amounts of computation and incur long processing times. In this work, we aim to accelerate inference and training of coordinate-based MLPs for implicit neural representations by proposing a new split MLP architecture, Co-ordX. With CoordX, the initial layers are split to learn each dimension of the input coordinates separately. The intermediate features are then fused by the last layers to generate the learned signal at the corresponding coordinate point. This significantly reduces the amount of computation required and leads to large speedups in training and inference, while achieving similar accuracy as the baseline MLP. This approach thus aims at first learning functions that are a decomposition of the original signal and then fusing them to generate the learned signal. Our proposed architecture can be generally used for many implicit neural representation tasks with no additional memory overheads. We demonstrate a speedup of up to 2.92x compared to the baseline model for image, video, and 3D shape representation and rendering tasks.

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Implicit Geometric Regularization for Learning Shapes

Cited by 62 publications

References 0 publications

TaylorImNet for Fast 3D Shape Reconstruction Based on Implicit Surface Function

TaylorImNet for Fast 3D Shape Reconstruction Based on Implicit Surface Function

Neural Implicit Surface Evolution using Differential Equations

CoordX: Accelerating Implicit Neural Representation with a Split MLP Architecture

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